Statics, structure, and residual normal moveout: Exact mathematical solutions in simple form

The separation of seismic reflection times into the component parts due to source static, receiver static, structure time, and residual normal moveout is exhibited in terms of simple differential and integral operations on the reflection time. The solution is valid for all component parts which possess an ${L_2}$ norm on the open one-dimensional domain of common midpoint. The equations yield simple, explicit solutions for each separate component. Possible methods of implementing these direct solutions for real travel-time data are presented with suggestions for avoiding, or bypassing, the differential operations. These solutions are presented both to provide a novel viewpoint for examining the so-called statics equation and as an aid to those who are actively pursuing the problem of finding methods for successfully optimizing statics problems in divers and diverse situations.